Classification rules based on coalitions explain multiple category assignments
Classification Aggregation with Multiple Memberships
Computer Science and Game TheoryMultiagent Systems
Summary
Sometimes people try to sort objects into categories by combining different opinions. This paper looks at the case when each person picks one category for an object, but the final decision can include several categories at once. The authors describe special rules, called 'junta rules,' where certain groups have the power to decide which categories are assigned. They use math concepts like coalitions and ultrafilters to explain how these decisions can be stable and fair. Their work also compares situations with many people to clarify these ideas.
What this means in practice
- •For decision making teams: Resolve how groups with overlapping decision rights assign multiple categories to items based on individual votes.
- •For online content moderators: Design aggregation rules that fairly combine multiple reviewers’ single- category labels into final multi-category tags.
A theory result. No direct application yet.
Authors
Federico Fioravanti, Leo Kurata, Vasilis Stamatis
Abstract
People face the problem of classifying objects into categories while aggregating their opinions. We axiomatically study such a classification aggregation problem with multiple memberships, meaning that each individual assigns one category to every object, whereas the resulting classification may assign more than one category. Under the natural settings and axioms (i.e., Independence and Supportiveness), each of our new axioms -- Responsibility, Split Stability and Rejection Stability -- characterises what we call the junta rules. The rules assign a category to an object exactly when some member of a fixed coalition does so. The coalitions that can secure an assignment form a grill, a topological structure implied by an ultrafilter. Hence, the study parallels the literature on Arrow's theorem characterised by the decisive coalition structures. An infinite population setting is also investigated to clarify the differences among the axioms.